Question

PQRS is a parallelogram. QM is the

perpendicular from Q to SR and QN is

the perpendicular from Q to PS. If SR = 12 cm

and QM = 6 cm, find the area of a parallelogram

PQRS. Also find QN if PS = 4 cm.​

Answer 1

${\large{\sf{\pmb{\underline{Understanding \; the \; question...}}}}}$

☀ According to the question, there is a parallelogram given and it named as PQRS . Guys, I attach a figure as attachment here, kindly see it too to understand the question properly.

☀ As PQRS is a parallelogram. QM is the height of this parallelogram. SR is base here. QM is the perpendicular from Q to SR and QN is the perpendicular from Q to PS If SR measure 12 cm and QM measure 6 cm, find the area of a parallelogram PQRS . Also find QN if PA measure 4 cm.

☀ What to find out?

We have to find out the area of this parallelogram.

And we have to find the measurement of QN too if PS is given as 4 centimetres.

${\large{\sf{\pmb{\underline{Given \; that...}}}}}$

$\begin{gathered}\begin{gathered}\bigstar \sf QM \: is \: the \: height \\ \\ \bigstar \sf QM \: measures \: 6 \: cm \\ \\ \bigstar \sf SR \: measures \: 12 \: cm \\ \\ \bigstar \sf SR \:is \: the\: base \\ \\ \bigstar \sf PS \: measures \: 4 \: cm\end{gathered} \end{gathered}$

${\large{\sf{\pmb{\underline{To \; find...}}}}}$

$\begin{gathered}\begin{gathered}\bigstar \sf Area \: of \: parallelogram \\ \\ \bigstar \sf Measurement \: of \: QN\end{gathered} \end{gathered}$

${\large{\sf{\pmb{\underline{Solution...}}}}}$

$\begin{gathered} \begin{gathered}\bigstar \sf Area \: of \: parallelogram \: = 72 \: cm^{2} \\ \\ \bigstar \sf Measurement \: of \: QN \: 18 \: cm\end{gathered} \end{gathered}$

${\large{\sf{\pmb{\underline{Using \; concepts...}}}}}$

$\begin{gathered}\begin{gathered}\bigstar \sf Area \: of \: parallelogram \: formula \\ \\ \bigstar \sf Measurement \: of \: QN \: formulas \: (atq)\end{gathered} \end{gathered}$

${\large{\sf{\pmb{\underline{Using \; formulas...}}}}}$

${\small{\underline{\boxed{\frak{Area \: of \: parallelogram \: = Base \times Height}}}}}$

${\small{\underline{\boxed{\frak{QN \: = \dfrac{Area \: of \: parallelogram}{PS \: measurement}}}}}}$

${\large{\sf{\pmb{\underline{Here,}}}}}$

$\begin{gathered}\begin{gathered}\bigstar \sf Area \: is \: ? \\ \\ \bigstar \sf Height \: is \: 12 \: cm \\ \\ \bigstar \sf Base \: is \: 12 \: cm \\ \\ \bigstar \sf PS \: = 4 \: cm \\ \\ \bigstar \sf Area \: is \: (Have \: to \: find)\end{gathered} \end{gathered}$

${\large{\sf{\pmb{\underline{Full \; Solution...}}}}}$

~ Firstly let us find the area of the parallelogram..!

↝ Area = Base × Height

↝ Area = 12 × 6

↝ Area = 72 cm²

Henceforth, 72 cm² is the area of the parallelogram.

~ Now let's find the measurement of QN..!

↝ QN = Area/PS

↝ QN = 72/4

↝ QN = 36/2

↝ QN = 18 cm

Henceforth, 18 cm is the measurement of QN.

Answer 2

Given : PQRS is a parallelogram. QM is the perpendicular from Q to SR and QN is the perpendicular from Q to PS.  

SR = 12 cm and QM = 6 cm,

To find :  the area of a parallelogram PQRS.

Also find QN if PS = 4 cm.​

Solution:

Area of parallogram = base * height

base SR  = 12 cm

QM = height = 6 cm

Area of parallelogram = 12 * 6 = 72 cm²

Also perpendicular on a side of parallelogram must be less than adjacent side of parallelogram  ( because adjacent side of parallelogram will be hypotenuse of right angle triangle formed)

=>  QM <  QR  and PS

=> 6  < QR  and PS

Given PS = 4 cm ( which is not possible )

Assuming QN = 4 cm  and then finding PS

=> PS * QN  = 72

=> PS * 4 = 72

=> PS = 18  cm

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